Exploring synchronized oscillations in Kuramoto-type oscillators with nonlinear feedback

Synchronization is a hallmark of complex systems, emerging from the interplay of randomness, coupling and nonlinear dynamics. In this project - carried out under the supervision of Prof Sitabhra Sinha of the Institute of Mathematical Sciences, Chennai - we explore synchronization in a system of coupled oscillators using the Kuramoto model, but with an additional nonlinear feedback term. We examine how frequency distributions, coupling strength and network topology influence synchronization. We study the time series of the phases of the oscillators for fully-connected, loosely-connected, directed and undirected networks, and also for different lattices (toroidal, square and hexagonal). Potential future applications of this work include gaining deeper insights into cardiac dynamics, circadian rhythms and the collective flashing patterns observed in certain species of fireflies.